Enhanced QPSK or DQPSK data demodulation for direct sequence spreading (DSS) system waveforms using orthogonal or near-orthogonal spreading sequences

ABSTRACT

A method of correcting phase error of a phase shift keyed (PSK) signal includes (a) receiving a signal modulated by a spreading sequence; (b) despreading the received signal using a receiver spreading sequence similar to the spreading sequence of step (a); (c) calculating a crosscorrelation profile between the receiver spreading sequence and the received signal; and (d) calculating an autocorrelation profile of the receiver spreading sequence to determine a spreading code property (SCP). The method also includes (e) estimating a timing error in alignment between the autocorrelation and the crosscorrelation profiles; and (f) correcting a phase error of the signal despread in step (c), by using the SCP and the estimated timing error.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims priority of U.S. Provisional Patent ApplicationSer. No. 60/703,316, filed Jul. 28, 2005.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

This invention was made with Government Support Under Agreement No.DAAB07-03-9-K601 awarded by the United States Army. The Government hascertain rights in the invention.

TECHNICAL FIELD

The present invention relates, in general, to communication systems.More specifically, it relates to enhanced QPSK or DQPSK datademodulation for direct sequence spreading (DSS) system waveforms usingorthogonal or near-orthogonal spreading sequences.

BACKGROUND OF THE INVENTION

Quadrature Phase Shift Keying (QPSK) data modulation is used to increasethe data rate capability over Binary Phase Shift Keying (BPSK) datamodulation. To improve data performance in multi-path channel conditionsand to reduce the transmit power spectral density, direct sequencespreading is applied to the data modulation. Differential data detectionis performed to simplify the demodulation process, resulting indifferential QPSK (DQPSK) reception. The existing 802.11b waveformprovides both DBPSK and DQPSK data modulation using a BPSK signal forthe direct sequence spreading to provide 1 and 2 Mbps data capability.

To achieve the 1 and 2 Mbps data rates, 11 chips are used to spread thedata modulated signal. An 11 chip Barker sequence is used for thespreading sequence. The 11 chip Barker sequence possesses excellentautocorrelation properties, providing a maximum correlation sidelobelevel of 1/11 the peak correlation value. To achieve this excellentcorrelation property on each data symbol, the same 11 chip Barkersequence is used to spread each data symbol.

As an alternative to using short repeated sequences, BPSK modulation maybe used to spread the data. BPSK provides a simple straight forwardmeans to spread either the BPSK or QPSK data. To meet the 802.11spectral requirements, the BPSK spread signal is passed through alowpass filter to reduce the power spectrum sidelobe level. The filteredBPSK signal is operated within the linear region of the power amplifierto minimize spectral regrowth output from the RF power amplifier.

There are, however, some limitations to using the aforementionedtechniques. First, waveforms using short spreading sequences, such asthe 11 chip Barker sequence used for 802.11b waveforms, limit the delayspread range for channel multi-path equalization, because two adjacentsymbols can be opposite in polarity. Further, short, repeated, spreadingsequences also enable unauthorized listeners to easily recover the datasymbol stream. Longer sequences remove these limitations. However,longer spreading sequences do not provide excellent autocorrelationproperties across short sections (11 chips for the 802.11b waveforms) ofthe spreading sequence. Degradation in the autocorrelation propertydirectly degrades the bit-error-rate (BER) system performance.

Second, BPSK spreading waveforms limit power efficiency at the RF poweramplifier, because they require the amplifier to operate in a linearmode to prevent spectral sidelobe regrowth. Spreading data usingconstant envelope modulation signals, like Minimum Shift Keying (MSK) ornear constant envelope modulation, like Quasi-bandlimited MSK (QBL-MSK)and Raised Cosine filtered Offset Quadrature Phase Shift Keying(RC-OQPSK), however, enable the RF power amplifier to operate in thenonlinear mode, increasing power efficiency.

Standard parallel demodulation techniques for MSK, QBL-MSK, and RC-OQPSKdespread the signal using independent I and Q sequences, and require twoorthogonal or near orthogonal spreading sequences. Gold codes aretypically used because of their good autocorrelation andcross-correlation properties. However, Gold codes also require, atminimum, 31 chips (lowest length Gold code) of spreading on both the Iand Q data, and increasing the number of chips results in a reduced datarate for the same operational chip rate. To reduce the number ofspreading chips required for these constant or near constant envelopemodulation signals, serial formatting is applied to the spreadingwaveform. Serial formatting combined with serial demodulation enablesthese waveforms to be demodulated similarly to BPSK.

For a serial despread MSK, QBL-MSK, or RC-OQPSK signal, the repeating 11chip Barker sequence can be used for the spreading sequence.Autocorrelation properties for the 11 chip Barker sequence areexcellent, providing suppression of the undesired serial demodulationterm. To avoid the limitations associated with the short spreadingsequence, a longer spreading sequence is used. As described previously,longer spreading sequences do not provide excellent autocorrelationproperties across short sections (11 chips for the 802.11b waveforms) ofthe spreading sequence. The poor autocorrelation properties associatedwith the long spreading sequence result in the undesired serialdemodulation term not being suppressed.

A BER performance curve with a maximum of a quarter chip timing error(sampling at twice the chip rate) for DQPSK data modulations withQBL-MSK spreading for a short 8 chip Neuman-Hoffman sequence (00001101)is shown in FIG. 1. As depicted in FIG. 1, for ideal timing (0 or 0.5Tc), a 10⁻⁶ BER is achieved at approximately Es/No equal to 11.9 dB,while the maximum Tc/4 timing error condition requires the Es/No toincrease to approximately 12.5 dB to provide the same bit error rate.

The BER performance curve with a maximum of a quarter chip timing error(sampling at twice the chip rate) for DQPSK data modulations withQBL-MSK spreading for a long, random spreading sequence is shown in FIG.2. As depicted in FIG. 2, for ideal timing (0 or 0.5 Tc), a 10⁻⁶ BER isachieved at approximately an Es/No equal to 12.5 dB, while the maximumTc/4 timing error condition requires the Es/No to increase toapproximately 16 dB to provide the same bit error rate. For idealtiming, the additional Es/No required for the long sequence versus theshort sequence is only 0.6 dB. For the maximum Tc/4 timing errorcondition, the additional Es/No required for the long sequence versusthe short sequence is 3.5 dB. This significant degradation in BERperformance for timing error must be reduced by either increasing thetiming resolution or by compensating for the poorer autocorrelationproperties of the long spreading sequence over the shorter symbolspreading length. Increasing the timing resolution requires an increasein the sampling rate, which increases the demodulator complexity and DCpower consumption.

To minimize demodulator complexity and power consumption, the presentinvention provides a compensation approach, among other features.

SUMMARY OF THE INVENTION

To meet this and other needs, and in view of its purposes, the presentinvention provides a method of correcting phase error of a phase shiftkeyed (PSK) signal, in a receiver. The method includes the steps of (a)receiving a signal modulated by a spreading sequence; (b) despreadingthe received signal using a receiver spreading sequence similar to thespreading sequence of step (a); (c) calculating a crosscorrelationprofile between the receiver spreading sequence and the received signal;(d) calculating an autocorrelation profile of the receiver spreadingsequence to determine a spreading code property (SCP); (e) estimating atiming error in alignment between the autocorrelation and thecrosscorrelation profiles; and (f) correcting a phase error of thesignal despread in step (c), by using the SCP and the estimated timingerror.

Another embodiment of the present invention provides a method ofserially demodulating a phase shift keyed (PSK) signal, in a receiver.The method includes (a) receiving a PSK signal modulated by a spreadingsequence at a chip rate; (b) dividing the PSK signal into an inphase (I)signal and a quadrature (Q) signal at a sampling rate greater than thechip rate; (c) rotating phases of the I signal and the Q signal at thesampling rate of step (b) to obtain serially demodulated I and Qsignals; (d) determining chip synchronization time for the seriallydemodulated I and Q signals; (e) decimating the serially demodulated Iand Q signals, based on the determined chip synchronization time, sothat the serially demodulated I and Q signals are sampled at the chiprate; and (f) despreading both the decimated I and Q signals by mixingboth the decimated I and Q signals with a single spreading sequence.

Yet another embodiment of the invention is a receiver. The receiverincludes a despreading module for despreading a baseband signal, using aspreading sequence generated by a code generator, a crosscorrelationmodule for calculating a crosscorrelation profile between the basebandsignal and the spreading sequence, an autocorrelation module forcalculating an autocorrelation profile of the spreading sequence todetermine a SCP value of the spreading sequence. The receiver alsoincludes a timing error estimating module, coupled to thecrosscorrelation and autocorrelation modules, for estimating analignment error between the autocorrelation profile and thecrosscorrelation profile; and a phase correction module, coupled to thetiming error estimating module and the despreading module, forcorrecting a phase error in the despread baseband signal.

It is understood that the foregoing general description and thefollowing detailed description are exemplary, but are not restrictive,of the invention.

BRIEF DESCRIPTION OF THE DRAWING

The invention is best understood from the following detailed descriptionwhen read in connection with the accompanying drawing. Included in thedrawing are the following figures:

FIG. 1 is a BER performance curve with a maximum of a quarter chiptiming error (sampling at twice the chip rate) for DQPSK datamodulations with QBL-MSK spreading for a short 8 chip Neuman-Hoffmansequence;

FIG. 2 is a BER performance curve with a maximum of a quarter chiptiming error (sampling at twice the chip rate) for DQPSK datamodulations with QBL-MSK spreading for a long, random spreadingsequence;

FIG. 3 is a block diagram of a phase correction module, in accordancewith an embodiment of the present invention;

FIGS. 4A and 4B are graphs depicting the improved BER performance forDQPSK data detection using the phase correction module of FIG. 3 versusDQPSK without phase correction;

FIGS. 5A, 5B and 5C are graphs illustrating severe envelope distortionsoccurring when both the I and Q signals go to zero at the same point intime;

FIGS. 6A, 6B and 6C are graphs illustrating minimal RF envelopedeviation occurring when the I and Q signals do not go to zero at thesame point in time;

FIG. 7 is a block diagram of an SQBL-MSK module of a transmitter, inaccordance with an embodiment of the present invention;

FIG. 8 is a block diagram of an SQBL-MSK demodulator front-end of areceiver, in accordance with an embodiment of the present invention;

FIG. 9 is a plot of a QBL-MSK autocorrelation function, in accordancewith an embodiment of the present invention;

FIG. 10 is a block diagram of an SQBL-MSK despreading operation, inaccordance with an embodiment of the present invention;

FIG. 11 is a block diagram of a phase rotator, in accordance with anembodiment of the present invention;

FIG. 12 is a block diagram of a modified phase rotator, in accordancewith an embodiment of the present invention;

FIG. 13 is a block diagram of a SYNC detection module, in accordancewith an embodiment of the present invention;

FIG. 14 is a plot of a SYNC correlation curve, for use with the SYNCdetection module of FIG. 13; and

FIG. 15 is a block diagram of a symbol detector with phase correctionmodule, in accordance with an embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

To enable operation of a serial demodulator with long spreadingsequences, the serial demodulator spreading operation takes advantage ofknowing the long spreading sequence. The spreading properties for thelong spreading sequence are determined for each short spreading sequenceused to despread the data. By knowing the spreading sequence propertyfor the despread data symbol along with an estimate of the chip timingerror from the synchronization correlation function, a proper phasecorrection is applied to the despread I and Q signals, significantlyreducing the undesired serial demodulation term.

FIG. 3 shows phase correction module 10. Module 10 is applied to thedespread inphase (I) and quadrature (Q) signals to generate the phasecorrected I(Ic) and Q(Qc) signals. As shown in FIG. 3, the despread Iand Q signals, I(n) and Q(n), enter phase correction module 10 and aremixed with a cos [θ(n)] signal at mixers 12 and 20 and a sin [θ(n)]signal at mixers 16 and 18. The outputs from mixers 12 and 16 are thencombined at summer 14. Likewise, the outputs from mixers 18 and 20 arecombined at summer 22. Phase corrected signals Ic and Qc are then outputfrom summers 14 and 22. The correction phase terms using the cosine andsine signals depend upon the spreading sequence one chipcross-correlation property across the despread symbol.

It will be understood that as used herein, a “summer” includes functionsof addition and subtraction.

Removing the undesired serial demodulation term results in significantimprovement in the bit rate error (BER) performance. FIGS. 4A and 4Bshow the improved BER performance for DQPSK data detection using thephase correction module versus DQPSK without phase correction.Specifically, FIG. 4A shows DQPSK BER performance with phase correctionand FIG. 4B shows DQPSK BER performance without phase correction. Theimprovement is shown for different chip timing errors. For example, fora Tc/4 timing error, approximately 13.5 dB is required to provide a 10⁻⁶BER for DQPSK with phase correction, whereas 16 dB is required toprovide the same bit error rate without phase correction. This is a 2.5dB reduction in Es/No. Further, for a Tc/4 timing error, the longsequence with phase correction requires an increase of 1 dB in Es/No ascompared to a short sequence for operation at 10⁻⁶ BER (compare FIGS. 4and 1).

An embodiment of the present invention uses serial QBL-MSK for spreadingmodulation to provide near constant RF envelope modulation and to enableuse of serial despreading. Although QBL-MSK is selected as the spreadingwaveform for this particular embodiment, other constant or near constantenvelope modulations, such as MSK, Gaussian MSK, OQPSK, and RC-OPSK maybe used.

Serial despreading, as opposed to parallel despreading, utilizes asimplified BPSK despreading operation and separates despreading intoinphase (I) and quadrature (Q) codes. Serial despreading reduces thechip to symbol rate to 8 chips per symbol. Lower spreading ratios, suchas 8 chips/symbol, are desirable for obtaining higher data rates whenthe communications channel can support it. For BPSK or QPSK datamodulation on SQBL-MSK, a spread modulation waveform may be written asfollows: $\begin{matrix}{\begin{matrix}{{s(t)} = {\sum\limits_{k = 0}^{N}\left\{ {{\left\lbrack {\sum\limits_{i = 0}^{M - 1}{\left( {- 1} \right)^{i}{c_{{2i} + {2{kM}}} \cdot p}\left( {t - {\left\lbrack {{2i} + {2{kM}}} \right\rbrack T_{c}}} \right)}} \right\rbrack{\cos\left( {{2\pi\quad f_{o}t} + \theta_{k}} \right)}} +} \right.}} \\\left. {\left\lbrack {\sum\limits_{i = 0}^{M - 1}{\left( {- 1} \right)^{i}{c_{{2i} + {2{kM}}} \cdot {p\left( {t - {\left\lbrack {{2i} + {2{kM}} + 1} \right\rbrack T_{c}}} \right)}}}} \right\rbrack{\sin\left( {{2p\quad f_{o}t} + \theta_{k}} \right)}} \right\}\end{matrix}{and}} & \left( {{eqn}\quad 1} \right) \\{{p(t)} = \left\{ {\begin{matrix}{\left\lbrack \frac{\sin\left( \frac{\pi\quad t}{2T_{c}} \right)}{\left( \frac{\pi\quad t}{2T_{c}} \right)} \right\rbrack^{3};} & {{{- 2}T_{c}} \leq t \leq {2T_{c}}} \\{0;} & {{elsewhere}.}\end{matrix};} \right.} & \left( {{eqn}\quad 2} \right)\end{matrix}$where T_(c) represents the chip period, c_(i) represents the chip attime iT_(c), 2M is the number of chips per data symbol in the modulatedsignal, p(t) is the QBL pulse-shaping function, f_(o) is the carriercenter frequency, and the (−1)^(i) terms, which multiply the chip value,represent the serial formatting. The chips (c;_(i)), which spread thedata modulated symbols (BPSK or QPSK), are either +1 or −1.

The data modulation (BPSK or QPSK), represented by the θ_(k) carrierphase term, is either 0 or π for BPSK data modulation and −0.5π, 0,0.5π, or π for QPSK data modulation. Applying differential encoding tothe BPSK or QPSK data modulation does not impact this equation, only themapping to the carrier phase term given by the following equation:$\begin{matrix}{{\theta_{k} = {\sum\limits_{m = 0}^{k}{\Delta\quad\theta_{m}}}};} & \left( {{eqn}\quad 3} \right)\end{matrix}$where Δθ is the phase change introduced by the differential encoding.

For BPSK data modulation, the SQBL-MSK spreading signal is not impactedby the data modulation. For QPSK data modulation, however, the SQBL-MSKspreading signal is impacted by the data modulation at the symbolboundary conditions when either a −0.5π (−90 degree) or 0.5π (90 degree)phase change between symbols occurs. Two different 90 degree phasechange boundaries associated with QPSK data modulation, where the pastQPSK symbol is at 0 degrees and the present QPSK symbol is at 90degrees, may be examined to show two significantly different RF envelopeeffects. Severe RF envelope distortion is shown in FIGS. 5A-5C. Asshown, when both the I and Q signal go to zero at the same point intime, the RF envelope goes to zero. Minimal RF envelope deviation,however, is shown in FIGS. 6A-6C. As shown, the I and Q signals do notgo to zero at the same point in time.

As shown in FIGS. 5A-5C, the near constant RF envelope performance ofSQBL-MSK is not preserved. To preserve the near constant RF envelopeperformance of SQBL-MSK, a phase mapping module may be provided in thetransmitter. The phase mapping module changes the phase trajectory onlyabout the symbol boundary. Since this change occurs only at the boundarycondition, the SQBL-MSK data modulation equation may be used, withoutphase mapping adjustment, to provide phase correction in the receiver bythe phase correction module shown in FIG. 15 (for example).

FIG. 7 shows a block diagram for SQBL-MSK modulator 32 of transmitter30, with I {x(t)} and Q {y(t)} data modulation of BPSK or QPSK withSQBL-MSK spreading on the data symbols. As shown, the I and Q datasignals are mixed with a carrier signal at mixers 34 and 38. The outputsfrom mixers 34 and 38 are then combined by summer 36. The resultingsignal is a baseband signal, s(t), represented by the followingequation:s(t)=x(t)cos(2 πf _(o) t)+y(t)sin(2 πf _(o) t).

Transmitter 30 transmits an RF modulated signal s(t). The RF modulatedsignal s(t) is then received by receiver 40 shown in FIG. 8.

The equations for the I {x(t)} and Q {y(t)} signals modulating thecarrier may be obtained from equation 1 as follows: $\begin{matrix}{\begin{matrix}{{x(t)} = {\sum\limits_{k = 0}^{N}\left\{ {{\left\lbrack {\sum\limits_{i = 0}^{M - 1}{\left( {- 1} \right)^{i}{c_{{2i} + {2{kM}}} \cdot p}\left( {t - {\left\lbrack {{2i} + {2{kM}}} \right\rbrack T_{c}}} \right)}} \right\rbrack{\cos\left( \theta_{k} \right)}} +} \right.}} \\\left. {\left\lbrack {\sum\limits_{i = 0}^{M - 1}{\left( {- 1} \right)^{i}{c_{{2i} + {2{kM}}} \cdot p}\left( {t - {\left\lbrack {{2i} + {2{kM}} + 1} \right\rbrack T_{c}}} \right)}} \right\rbrack{\sin\left( \theta_{k} \right)}} \right\}\end{matrix}{and}} & \left( {{eqn}\quad 4} \right) \\\begin{matrix}{{y(t)} = {\sum\limits_{k = 0}^{N}\left\{ {{\left\lbrack {\sum\limits_{i = 0}^{M - 1}{\left( {- 1} \right)^{i}{c_{{2i} + {2{kM}}} \cdot p}\left( {t - {\left\lbrack {{2i} + {2{kM}}} \right\rbrack T_{c}}} \right)}} \right\rbrack{\sin\left( \theta_{k} \right)}} +} \right.}} \\{\left. {\left\lbrack {\sum\limits_{i = 0}^{M - 1}{\left( {- 1} \right)^{i}{c_{{2i} + {2{kM}}} \cdot p}\left( {t - {\left\lbrack {{2i} + {2{kM}} + 1} \right\rbrack T_{c}}} \right)}} \right\rbrack{\cos\left( \theta_{k} \right)}} \right\}.}\end{matrix} & \left( {{eqn}\quad 5} \right)\end{matrix}$

Since the data symbol phase for QPSK or DQPSK is equal to −90, 0, 90, or180 degrees over each symbol period, either the even spreading sequencechips are on I with the odd chips on Q (0 and 180 degree symbolconditions) or the odd spreading sequence chips are on I with the evenchips on Q (−90 and 90 degree symbol conditions).

FIG. 8 shows a block diagram for SQBL-MSK demodulator 42 of receiver 40.The demodulator front-end down-converts the received signal to basebandI and Q signals, digitizes the I and Q signals, and digitally filtersthe I and Q signals with chip matched filters. As shown, the receivedsignal is mixed by mixers 44 and 46 with respective quadrature signalsat the carrier frequency, resulting in the desired baseband I and Qsignals (mixing difference term) and the undesired signal at twice thecarrier frequency (mixing sum term). Lowpass filtering by LPF 48 and LPF50 follows the down-converter function to remove the undesired mixingsummation term. Baseband I and Q signals are digitized by the I and Qanalog-to-digital converters (ADC), shown as ADC 52 and 54. As shown,the sampling rate of the ADC is equal to twice the chip rate. Followingdigitization, the I and Q signals are filtered, respectively, by chipmatched filters 56 and 58, which maximize the signal-to-noise ratio(SNR). The I and Q chip matched filter outputs are then sent to thedespreading operation shown in FIG. 10.

The QBL-MSK chip matched filter coefficients are based on the QBL-MSKpulse-shaping function defined by: $\begin{matrix}{{p(t)} = \left\{ \begin{matrix}{\left\lbrack \frac{\sin\left( \frac{\pi\left\lbrack {t - {2T_{c}}} \right\rbrack}{2T_{c}} \right)}{\left( \frac{\pi\left\lbrack {t - {2T_{c}}} \right\rbrack}{2T_{c}} \right)} \right\rbrack^{3};} & {0 \leq t \leq {4T_{c}}} \\{0;} & {{elsewhere}.}\end{matrix} \right.} & \left( {{eqn}\quad 6} \right)\end{matrix}$where T_(c) corresponds to the chip or symbol period.

Since the QBL-MSK pulse-shaping function is non-zero over a four chipperiod interval, the digital QBL-MSK chip matched filter operating attwice the chip rate may include 9 samples, defined by the followingequation: $\begin{matrix}{{{{p(k)} = \left\lbrack \frac{\left( \frac{\pi\left\lbrack {{0.5 \cdot k} - 2} \right\rbrack}{2} \right)}{\left( \frac{\pi\left\lbrack {{0.5 \cdot k} - 2} \right\rbrack}{2} \right)} \right\rbrack^{3}};\quad{k = 0}},1,2,3,\ldots\quad,8.} & \left( {{eqn}\quad 7} \right)\end{matrix}$

Recognizing that the filter value for k equal to 0 and 8 is zero, thedigital QBL-MSK chip matched filter response may be simplified to 7samples, as defined by the following equation: $\begin{matrix}{{{{{p(k)}\quad = \quad\left\lbrack \frac{\left( \frac{\pi\left\lbrack {{0.5 \cdot k}\quad - \quad 1.5} \right\rbrack}{2} \right)}{\left( \frac{\pi\left\lbrack {{0.5 \cdot k}\quad - 1.5} \right\rbrack}{2} \right)} \right\rbrack^{3}};\quad{k\quad = \quad 0}},\quad 1,\quad 2,\quad 3,\quad\ldots\quad,\quad 6.}\quad} & \left( {{eqn}\quad 8} \right)\end{matrix}$

Convolution of the QBL-MSK chip pulse shape with the QBL-MSK chipmatched filter results in a QBL-MSK autocorrelation function {g(t)}.FIG. 9 shows a plot of the QBL-MSK autocorrelation function {g(t)}. Asshown, the autocorrelation function is zero at time 2.5T_(c) away fromthe desired optimum sampling point (time 0).

Using the QBL-MSK autocorrelation function {g(t)}, the I and Q signals,shown in FIG. 8 as x₂(0.5*nT_(c)) and y₂(0.5*nT_(c)), respectively,output from chip matched filters 56 and 58 (based on equations 4 and 5)are as follows: $\begin{matrix}{\begin{matrix}{{x_{2}\left( {0.5\quad{nT}_{c}} \right)} = {\sum\limits_{k = 0}^{N}\left\{ {{\left\lbrack {\sum\limits_{i = 0}^{M - 1}{\left( {- 1} \right)^{i}{c_{{2i} + {2{kM}}} \cdot {g\left( {{0.5\quad{nT}_{c}} - {\left\lbrack {{2i} + {2{kM}}} \right\rbrack T_{c}}} \right)}}}} \right\rbrack{\cos\left( {\theta_{k} + \phi} \right)}} +} \right.}} \\\left. {\left\lbrack {\sum\limits_{i = 0}^{M - 1}{\left( {- 1} \right)^{i}{c_{{2i} + {2{kM}}} \cdot {g\left( {{0.5\quad{nT}_{c}} - {\left\lbrack {{2i} + {2{kM}} + 1} \right\rbrack T_{c}}} \right)}}}} \right\rbrack{\sin\left( {\theta_{k} + \phi} \right)}} \right\}\end{matrix}{and}} & \left( {{eqn}\quad 9} \right) \\\begin{matrix}{{y_{2}\left( {0.5\quad{nT}_{c}} \right)} = {\sum\limits_{k = 0}^{N}\left\{ {{\left\lbrack {\sum\limits_{i = 0}^{M - 1}{\left( {- 1} \right)^{i}{c_{{2i} + {2{kM}}} \cdot p}\left( {t - {\left\lbrack {{2i} + {2{kM}}} \right\rbrack T_{c}}} \right)}} \right\rbrack{\sin\left( {\theta_{k} + \phi} \right)}} +} \right.}} \\{\left. {\left\lbrack {\sum\limits_{i = 0}^{M - 1}{\left( {- 1} \right)^{i}{c_{{2i} + {2{kM}}} \cdot p}\left( {t - {\left\lbrack {{2i} + {2{kM}} + 1} \right\rbrack T_{c}}} \right)}} \right\rbrack{\cos\left( {\theta_{k} + \phi} \right)}} \right\};}\end{matrix} & \left( {{eqn}\quad 10} \right)\end{matrix}$where φ is the carrier phase error and θ_(k) is the phase introduced bydata symbol modulation.

FIG. 10 shows a block diagram of an SQBL-MSK despreading operation,which performs serial demodulation using phase rotator 60 anddespreading of the data symbols via despreader 64. As shown in FIG. 10,the I and Q chip matched filter outputs, shown in FIG. 8, enter phaserotator 60, described in more detail below. Phase rotator 60 enables theSQBL-MSK spread signal to be serially demodulated.

Thus, the present invention enables despreading of both the I and Qsignals using the same spreading sequence, eliminating the requirementof separating the spreading sequence into even and odd chips, asrequired by parallel despreaders. As shown in FIG. 10, despreadingmodule 64 uses the same spreading sequence (c_(n)) to despread both theI and Q signals.

The two samples per chip I and Q signals output from the phase rotatorare sent to the SYNC detection module shown in FIG. 13, which determinesthe timing control for selecting the proper sample and sent to decimator62, which reduces the sample rate for the despread operation to the chiprate. Decimator 62 decimates the I and Q signals by 2, providing signalsat the chip rate. The signals are then sent to despreader 64, where theI and Q signals are mixed with a single code, c_(n), from spreadingsequence generator 68 (module 66 provides a non-return to zero (NR2)translation of the c_(n) code).

The despread I and Q signals are then accumulated, over the data symbolperiod, which may consist of 2M chips per symbol, for example, byaccumulators 70 and 72. In this example, with 8 chips per symbol, M isequal to 4, which corresponds to 4 even and 4 odd chips per symbol.Switches 74 and 76 are closed at the symbol rate, kT_(s), providing thedetected I and Q symbol signals. The detected symbols are sent to thephase correction module shown in FIG. 15.

The phase rotator module shown in FIG. 10 may be easily implemented forDQPSK symbol detection. Implementation of the phase rotator is requiredto allow serial demodulation. A description of phase rotators which maybe implemented by the present invention are described by reference toFIGS. 11 and 12.

FIG. 11 shows phase rotator 60A for serial demodulation about afrequency of one quarter the chip rate below the carrier frequency,represented by −0.25*R_(c), where R_(c) represents the chip rate.Sampling at twice the chip rate corresponds to N equal to 2. As shown inFIG. 11, the I and Q chip matched filter outputs of FIG. 8, representedby x₂(nT_(c)/N) and y₂(nT_(c)/N), enter the phase rotator to be mixedwith a cos(πn/2N) signal at mixers 82 and 92 and a sin(πn/2N) signal atmixers 86 and 88. The outputs from mixers 82 and 86 are combined bysummer 84 and the outputs from mixers 88 and 92 are combined by summer90. The serial I {sx(n)} and Q {sy(n)} signals output from the phaserotator for N samples per chip, are sent to the SYNC detection moduleshown in FIG. 13 and the decimator shown in FIG. 10.

The serial I {sx(n)} and Q {sy(n)} signals output from the phase rotatorfor N samples per chip are related to the input I {x₂(n)} and Q{y₂(n)}signals by the following complex equation: $\begin{matrix}{{{{sx}\left( \frac{{nT}_{c}}{N} \right)} + {j\quad{{sy}\left( \frac{{nT}_{c}}{N} \right)}}} = {\left\lbrack {{x_{2}\left( \frac{{nT}_{c}}{N} \right)} + {j\quad{y_{2}\left( \frac{{nT}_{c}}{N} \right)}}} \right\rbrack \cdot {{\exp\left( {{- j}\quad 2{{\pi\left\lbrack \frac{R_{c}}{4} \right\rbrack}\left\lbrack \frac{{nT}_{c}}{N} \right\rbrack}} \right)}.}}} & \left( {{eqn}\quad 11} \right)\end{matrix}$

As shown by this equation, the phase rotator provides a rotatingexponential vector at the desired frequency −0.25*R_(c), represented bythe exponential term. Since R_(c)·T_(c)=1, the equation for the serial Iand Q signal output from the phase rotator may be rewritten, as follows,for N equal to 2: $\begin{matrix}{{{{sx}\left( {0.5\quad{nT}_{c}} \right)} + {j\quad{{sy}\left( {0.5\quad{nT}_{c}} \right)}}} = {\left\lbrack {{x_{2}\left( {0.5\quad{nT}_{c}} \right)} + {j\quad{y_{2}\left( {0.5\quad{nT}_{c}} \right)}}} \right\rbrack \cdot {{\exp\left( {{- j}\frac{\pi\quad n}{4}} \right)}.}}} & \left( {{eqn}\quad 12} \right)\end{matrix}$

When the present invention uses a receiver sampling rate equal to twicethe chip rate, the rotating vector changes by −45 degrees for eachsample. For a receiver with a sampling rate equal to the chip rate, therotating exponential vector changes by −90 degrees for each sample. ForN=1, the phase rotator operation requires only a +1, or −1multiplication operation on the I and Q input signals, followed by amapping module to the appropriate I or Q output. This phase rotatorstructure may easily be implemented in hardware.

The present invention may use a sampling rate that is twice the datarate, corresponding to N=2. For N=2, the phase rotator for even samplesis the is same as described for N=1. Odd samples require a 0.7071 or−0.7071 multiplication along with an addition operation, which resultsin a more complicated phase rotator structure.

Since the serial I and Q signals output from the phase rotator aredecimated by 2 before despreading by selecting either the even or oddsamples, the same phase rotation may be applied to both the even and oddsamples. The present invention simplifies the phase rotator module forN=2 by introducing a phase term, as shown in the following equation:$\begin{matrix}{{{{sx}\left( {0.5\quad{nT}_{c}} \right)} + {j\quad{{sy}\left( {0.5\quad{nT}_{c}} \right)}}} = {\left\lbrack {{x_{2}\left( {0.5\quad{nT}_{c}} \right)} + {j\quad{y_{2}\left( {0.5\quad{nT}_{c}} \right)}}} \right\rbrack \cdot {{\exp\left( {{- j}\frac{\pi\quad{INT}\left\{ {0.5 \cdot n} \right\}}{2}} \right)}.}}} & \left( {{eqn}\quad 13} \right)\end{matrix}$where INT represents a function that takes only the integer value of itsargument. Separating the samples into even and odd samples results inthe following two equations: $\begin{matrix}{{{{{{sx}\left( {nT}_{c} \right)} + {j\quad{{sy}\left( {nT}_{c} \right)}}} = {\left\lbrack {{x_{2}\left( {nT}_{c} \right)} + {j\quad{y_{2}\left( {nT}_{c} \right)}}} \right\rbrack \cdot {\exp\left( {{- j}\frac{\pi\quad n}{2}} \right)}}};}{{for}\quad{even}\quad{samples}\quad{and}}} & \left( {{eqn}\quad 14} \right) \\{{{{{{sx}\left( {\left\lbrack {0.5 + n} \right\rbrack T_{c}} \right)} + {j\quad{{sy}\left( {\left\lbrack {0.5 + n} \right\rbrack T_{c}} \right)}}} = {\left\lbrack \quad{{x_{2}\left( {\left\lbrack {0.5 + n} \right\rbrack T_{c}} \right)} + {j\quad{y_{2}\left( {\left\lbrack {0.5 + n} \right\rbrack T_{c}} \right)}}} \right\rbrack \cdot {\exp\left( {{- j}\frac{\pi\quad n}{2}} \right)}}};}{{for}\quad{odd}\quad{{samples}.}}} & \left( {{eqn}\quad 15} \right)\end{matrix}$

Comparing the modified phase rotator of equations 14 and 15 to the phaserotator shown in FIG. 11, the even samples output from both rotators arethe same. However, the odd samples output from the modified phaserotator are rotated by 45 degrees (π/4 radians) from the odd samples ofthe phase rotator of FIG. 11. By adding the phase term, which is zerodegrees for even samples and 45 degrees (π/4 radians) for odd samples,the same simplified phase rotator structure associated with the N=1phase rotator may be obtained. FIG. 12 shows this modified phase rotatorstructure.

As shown in FIG. 12, the I and Q chip matched filter outputs of FIG. 8,represented by x₂(0.5nT_(c)) and y₂(0.5nT_(c)), enter phase rotator 60Bto be mixed with a cos(πINT{0.5n}/2) signal at mixers 102 and 112 and asin(πINT{0.5n}/2) signal at mixers 106 and 108. The outputs from mixers102 and 106 are then sent to summer 104 and the outputs from mixers 108and 112 are sent to summer 110. The serial I {sx(0.5n)} and Q {sy(0.5n)} signals output from phase rotator 60B, represented in FIG. 12 bysx(0.5nTC) and sy(0.5nTC), are sent to the SYNC detection module shownin FIG. 13 and decimator 62 shown in FIG. 10.

The modified phase rotator 60B provides a repetitive mapping structureof 8 samples on both the serial I and Q signals, as shown below:sx(0.5nT _(c))={x ₂(0), x ₂(0.5T _(c)), y ₂(T _(c)), y ₂(1.5T _(c)), −x₂(2T _(c)), −x ₂(2.5T _(c)), −y ₂(3T _(c)), −y ₂(3.5T _(c)), . . .}  (eqn 16)andsy(0.5nT _(c))={y ₂(0), y ₂(0.5T ^(c)), −x ₂(T _(c)), −x ₂(1.5T _(c)),−y ₂(2T _(c)), −y ₂(2.5T _(c)), x ₂(3T _(c)), x ₂(3.5T _(c)), . . . .}  (eqn 17)

Following the phase rotator operation is the sample rate reduction bydecimator 62 of FIG. 10. The decimation allows for selecting either theodd samples, [(n+0.5)T_(c)], or even samples (nT_(c)). The timing isdetermined by the SYNC detection operation.

The SYNC detection operation used to determine the proper timing willnow be described with reference to FIG. 13. The SYNC detection moduledetermines the proper selection of the I and Q samples to thedespreading operation and the timing error information for use by thephase correction module shown in FIG. 15. It will be appreciated that inthe example of FIG. 13, 128 chips are shown. Other numbers of chips mayalso be used.

Reduction in the complexity of the SYNC detection I and Q correlators isachieved by decimating the I and Q samples by a factor of 2. Decimationreduces the I and Q sampling rate so that it equals the chip rate. Thisdecimation is achieved by selecting either the even or odd samples to besent to the SYNC detection.

As shown in FIG. 13, the sample period for the input correlator signalis specified by T_(sa), which is equal to one half the chip period(T_(sa)=0.5·T_(c)) for operation of the SYNC detection at twice the chiprate. For operation of the SYNC detection module at the chip rate, thesample period equals the chip period (T_(s)=T_(c)). For operation of theSYNC detection at either the chip rate or twice the chip rate, the delayelements in the correlators 120 and 142 are specified by the chip period(T_(c)). For operating the SYNC detection algorithm at twice the chiprate, the delay element is implemented by two sample period delays(2·T_(sa)). For operating the SYNC detection algorithm at the chip rate,the delay element is implemented by a single sample period delay(T_(sa)).

The chip sliding correlators 120 and 142 for the input I and Q signals,as exemplified in FIG. 13, include a sliding length of 128 chips,represented by delay elements 122, 124, 126, 128 and 130 in FIG. 13,which are, respectively, coupled to mixers 132, 134, 136, 138 and 140for multiplication with respective spreading code signals of c₁₂₇, c₁₂₆,c₁₂₅, . . . , c₀. The 128 mixed signals are summed by summer 139. ThisSYNC length is not unique to the present invention and may be madeshorter or longer. Also, the full 128 chip correlation does not need tobe coherently combined over the full 128 chip sequence. For example, the128 chip correlation may be coherently combined over 32 chip segmentsfollowed by a noncoherent combining of the four 32 chip segments.Neither the SYNC sequence length, nor the correlation structure, isunique to the QPSK/DQPSK phase correction process.

As shown in FIG. 13, the I and Q correlator output signals are,respectively, squared by squaring functions 144 and 146, then combinedby summer 148. SYNC detection, it will be understood, may be determinedby using either the square of the correlation output or the correlationoutput (generated by square root module 150). Either correlation outputmay be used.

Typically, the correlation output is selected by switch 152, because itmay be easily implemented with the following approximation:$\begin{matrix}{{{{COR}(n)} = {{{Max}\left\{ {{{MAG}\left\lbrack {{ICOR}(n)} \right\rbrack},{{MAG}\left\lbrack {{QCOR}(n)} \right\rbrack}} \right\}} + {{\frac{1}{2} \cdot {Min}}\left\{ {{{MAG}\left\lbrack {{ICOR}(n)} \right\rbrack},{{MAG}\left\lbrack {{QCOR}(n)} \right\rbrack}} \right\}}}};} & \left( {{egn}\quad 18} \right)\end{matrix}$where Max{ } is the maximum value of its two arguments, Min{ } is theminimum value of its two arguments, and Mag[ ] is the magnitude of itsargument.

The signal used as an input signal to peak detection module 154, foreach of the two different correlation outputs are shown in FIG. 14. Forthe square-root output, the correlation signal to the peak detector isthe QBL-MSK autocorrelation function, while the squared output is thesquare of the QBL-MSK autocorrelation function. As may be seen, thecorrelation response for the squared QBL-MSK autocorrelation function issharper than the QBL-MSK autocorrelation function, as expected.

Since the correlation response is different depending on the inputsignal, the time error estimation is also dependent on which inputsignal is used. By comparing the amplitude of three adjacent samples,peak detection module 154 determines if a peak has occurred at thecenter sample. If the center sample is declared to be a peak, themagnitude of that sample (peak sample) is compared to the SYNC thresholdby SYNC detection comparison module 156. If the magnitude of the peaksample is greater than the SYNC threshold, SYNC is declared by the SYNCdetect signal sent to sample timing selection module 162.

SYNC determines the time location of the first chip and whether even orodd samples are processed in the despreader. If the SYNC process isoperated at twice the chip rate, a SYNC point within ±0.25·T_(c) isdetermined directly by the peak detection. For the SYNC processoperating at the chip rate, the SYNC detection point along with thecorrelation profile is used to establish the SYNC point within aresolution of ±0.25·T_(c), as described below.

Using the correlation output based on the QBL-MSK autocorrelationresponse of FIG. 14 and operating the SYNC detection at the chip rate,an exemplary mapping to obtain a finer timing resolution (±0.25·T_(c))is outlined below:

-   -   (a) select sample nT_(c)−0.5T_(c) if COR(n−1)≧2·COR(n+1); −Tc/2        correction implemented (odd sample before the even sample used        in the SYNC detection) or    -   (b) select sample nT_(c)+0.5T_(c) if COR(n+1)≧2·COR(n−1); +Tc/2        correction implemented (odd sample after the even sample used in        the SYNC detection) or    -   (c) select sample nT_(c); no correction if neither of the two        above conditions is met;        where the SYNC I and Q inputs are the even samples only,        COR(nT_(c)) is the peak location, COR([n+1]T_(c)) is the sample        following the peak, and COR([n−1]T_(c)) is the sample before the        peak. In this manner, sample timing selection module 162 chooses        the even or the odd samples, based on these three relationships.        In is addition, from these three relationships the proper        samples output from phase rotator 60 in FIG. 10 may be sent to        despreader 64.

The timing error estimate provided by estimate timing error module 160,shown in FIG. 13, will now be described. For phase correction with SYNCoperating at a sample rate equal to the chip rate, 7 unique correlationconditions defined by X1, X2, and so on, to X7 are determined fromCOR(n), COR(n−1), and COR(n+1). Definitions of the seven correlationcondition are given below: $\begin{matrix}{{X\quad 1} = \left\{ {\begin{matrix}{1;{{{if}\quad{{COR}\left( {n - 1} \right)}} > {{COR}\left( {n + 1} \right)}}} \\{0;{{{if}\quad{{COR}\left( {n - 1} \right)}} \leq {{COR}\left( {n + 1} \right)}}}\end{matrix},} \right.} & \left( {{eqn}\quad 19} \right) \\{{X\quad 2} = \left\{ {\begin{matrix}{1;{{{if}\quad{{COR}\left( {n - 1} \right)}} > {2 \cdot {{COR}\left( {n + 1} \right)}}}} \\{0;{{{if}\quad{{COR}\left( {n - 1} \right)}} \leq {2 \cdot {{COR}\left( {n + 1} \right)}}}}\end{matrix},} \right.} & \left( {{eqn}\quad 20} \right) \\{{X\quad 3} = \left\{ {\begin{matrix}{1;{{{if}\quad{{COR}\left( {n + 1} \right)}} > {2 \cdot {{COR}\left( {n - 1} \right)}}}} \\{0;{{{if}\quad{{COR}\left( {n + 1} \right)}} \leq {2 \cdot {{COR}\left( {n - 1} \right)}}}}\end{matrix},} \right.} & \left( {{eqn}\quad 21} \right) \\{{X\quad 4} = \left\{ {\begin{matrix}{1;{{{if}\quad{{COR}\left( {n - 1} \right)}} > {3 \cdot {{COR}\left( {n + 1} \right)}}}} \\{0;{{{if}\quad{{COR}\left( {n - 1} \right)}} \leq {3 \cdot {{COR}\left( {n + 1} \right)}}}}\end{matrix},} \right.} & \left( {{eqn}\quad 22} \right) \\{{X\quad 5} = \left\{ {\begin{matrix}{1;{{{if}\quad{{COR}\left( {n + 1} \right)}} > {3 \cdot {{COR}\left( {n - 1} \right)}}}} \\{0;{{{if}\quad{{COR}\left( {n + 1} \right)}} \leq {3 \cdot {{COR}\left( {n - 1} \right)}}}}\end{matrix},} \right.} & \left( {{eqn}\quad 23} \right) \\{{X\quad 6} = \left\{ {\begin{matrix}{1;{{{if}\quad{1.25 \cdot {{COR}\left( {n + 1} \right)}}} < {{COR}\left( {n - 1} \right)} < {2 \cdot {{COR}\left( {n + 1} \right)}}}} \\{0;{otherwise}}\end{matrix},{and}} \right.} & \left( {{eqn}\quad 24} \right) \\{{X\quad 7} = \left\{ {\begin{matrix}{1;{{{if}\quad{1.25 \cdot {{COR}\left( {n - 1} \right)}}} < {{COR}\left( {n + 1} \right)} < {2 \cdot {{COR}\left( {n - 1} \right)}}}} \\{0;{otherwise}}\end{matrix}.} \right.} & \left( {{eqn}\quad 25} \right)\end{matrix}$

These seven different correlation conditions are further processed usingthe following three digital relationships:Y1=X2 OR X3,  (eqn 26)Y2=X4 OR X5,  (eqn 27)andY3=X6 OR X7.  (eqn 28)

The four phase correction parameters X1, Y1, Y2, and Y3 are sent tophase correction table 186, shown in FIG. 15.

It will be understood that SYNC establishes initial timing for thedespreading and demodulation processes. To maintain timing throughoutthe waveform, either chip tracking or serial probes may be used. Chiptracking uses early, late, and on-time despreading to estimate thetiming error and perform the proper timing correction. For the chiptracking implementation, information from the early, late, and on-timedespreaders may also be used to provide the timing error estimation tothe phase correction module.

The serial probe approach is easily implemented, since it is performedin the same manner as SYNC detection process shown in FIG. 13. A knownsequence is used for the serial probe, just like with SYNC detection.The serial probe is inserted into the waveform and used to provide anupdate on the chip timing and the timing error estimation for the phasecorrection module. The advantage of the SYNC detection and serial probeapproach is that a known sequence may be used to determine tap positionsfor RAKE detection in order to enhance performance in a multi-pathchannel.

During SYNC detection, a correlation profile based on peak correlationlevels are determined about the SYNC point established by correlationmemory module 158. The time interval over which this profile isgenerated is referred to as the multi-path window. Based on magnitudepeak level of the correlation profile, multi-path RAKE taps are selectedwith chip timing and timing error estimation for the phase correctionmodule for each tap.

Returning now to FIG. 10, despreading of the I and Q symbols is done atthe chip rate and timing set by the SYNC detection and serial probe,assuming the serial probe is used for maintaining chip timing. As shownin FIG. 10, the same spreading sequence (c_(n)) is used to despread theI and Q signals. The despread I and Q signal are accumulated over thedata symbol period, which includes 2M chips per symbol, as an example.For a RAKE implementation, chip timing at decimator 62, despreading atdespreader 64, and accumulation at accumulation modules 70 and 72, shownin FIG. 10, may be implemented individually for each RAKE tap based onindependent chip timing. Similarly, the spreading code alignment may bebased on RAKE tap calculation in a SYNC/serial probe function. Each raketap, it will be appreciated, generates a detected I and Q symbol signaloutput.

A general description of the phase error correction process, implementedby the present invention, will now be described. The serial I and Qoutputs from phase rotator 60 and decimator 62 may be rewritten asfollows: $\begin{matrix}{{{{sx}\left( {nT}_{c} \right)} = {{{x_{2}\left( {{nT}_{c} + {\Delta\quad T_{c}}} \right)} \cdot {\cos\left( \frac{\pi\quad n}{2} \right)}} + {{y_{2}\left( {{nT}_{c} + {\Delta\quad T_{c}}} \right)} \cdot {\sin\left( \frac{\pi\quad n}{2} \right)}}}}{and}} & \left( {{eqn}\quad 29} \right) \\{{{{sy}\left( {nT}_{c} \right)} = {{{- {x_{2}\left( {{nT}_{c} + {\Delta\quad T_{c}}} \right)}} \cdot {\sin\left( \frac{\pi\quad n}{2} \right)}} + {{y_{2}\left( {{nT}_{c} + {\Delta\quad T_{c}}} \right)} \cdot {\cos\left( \frac{\pi\quad n}{2} \right)}}}};} & \left( {{eqn}\quad 30} \right)\end{matrix}$where ΔTc is the timing error (±T_(c)/4 maximum) not removed by the SYNCtiming correction when, selecting the even or odd samples, based ontiming selection module 162 of FIG. 13. Inserting the equations forx₂(nT_(c)) and y₂(nT_(c)) and applying simplifications to theseequations provides the following expressions: $\begin{matrix}{{{{sx}\left( {nT}_{c} \right)} = {\sum\limits_{k = 0}^{N}\left\{ {{\left\lbrack {\sum\limits_{i = 0}^{{2M} - 1}{c_{i + {2{kM}}} \cdot {g\left( {\left\lbrack {{nT}_{c} + {\Delta\quad T_{c}}} \right\rbrack - {\left\lbrack {i + {2{kM}}} \right\rbrack T_{c}}} \right)} \cdot {\cos\left( \quad\frac{\pi\left\lbrack {{nT}_{c} - {\left\lbrack {i + {2{kM}}} \right\rbrack T_{c}}} \right\rbrack}{2T_{c}} \right)}}} \right\rbrack\quad{\cos\left( \quad{\theta_{k} + \quad\phi} \right)}} - {\left\lbrack \quad{\sum\limits_{i = 0}^{M - 1}\quad{c_{i + {2{kM}}}\quad \cdot {g\left( {\left\lbrack {{nT}_{c} + {\Delta\quad T_{c}}} \right\rbrack - {\left\lbrack {i + {2{kM}}} \right\rbrack T_{c}}} \right)} \cdot {\sin\left( \frac{\pi\left\lbrack {{nT}_{c} - {\left\lbrack {i + {2{kM}}} \right\rbrack T_{c}}} \right.}{2T_{c}} \right)}}} \right\rbrack{\sin\left( {\theta_{k} + \phi} \right)}}} \right\}}}{and}} & \left( {{eqn}\quad 31} \right) \\{{{sy}\left( {nT}_{c} \right)} = {- {\sum\limits_{k = 0}^{N}{\left\{ {{\left\lbrack {\sum\limits_{i = 0}^{{2M} - 1}{c_{i + {2{kM}}} \cdot {g\left( {\left\lbrack {{nT}_{c} + {\Delta\quad T_{c}}} \right\rbrack - {\left\lbrack {i + {2{kM}}} \right\rbrack T_{c}}} \right)} \cdot {\cos\left( \quad\frac{\pi\left\lbrack {{nT}_{c} - {\left\lbrack {i + {2{kM}}} \right\rbrack T_{c}}} \right\rbrack}{2T_{c}} \right)}}} \right\rbrack\quad{\sin\left( \quad{\theta_{k} + \quad\phi} \right)}} + {\left\lbrack \quad{\sum\limits_{i = 0}^{M - 1}\quad{c_{i + {2{kM}}}\quad \cdot {g\left( {\left\lbrack {{nT}_{c} + {\Delta\quad T_{c}}} \right\rbrack - {\left\lbrack {i + {2{kM}}} \right\rbrack T_{c}}} \right)} \cdot {\sin\left( \frac{\pi\left\lbrack {{nT}_{c} - {\left\lbrack {i + {2{kM}}} \right\rbrack T_{c}}} \right\rbrack}{2T_{c}} \right)}}} \right\rbrack{\cos\left( {\theta_{k} + \phi} \right)}}} \right\}.}}}} & \left( {{eqn}\quad 32} \right)\end{matrix}$

From these expressions, two key features of serial demodulation may beseen. First, the serial formatting factor (−1)^(i) shown in themodulation equation (eqn 1) is removed. Second, the I and Q basebandsignals consist of the filtered spreading sequence multiplied by eithera cosine or sine weighting function. For coherent detection, the cosineweighted filtered spreading sequence is the desired term on both the Iand Q signals.

The QBL-MSK autocorrelation function is nonzero for ±2.5 T_(c) about theideal SYNC time of zero (see FIG. 9). Since the cosine weightingfunction forces the QBL-MSK autocorrelation function to zero at times−Tc+ΔT_(c) and T_(c)+ΔT_(c), only the QBL-MSK terms at −2T_(c)+ΔT_(c),ΔT_(c), and 2T_(c)+ΔT_(c) are considered for each cosine weightedQBL-MSK autocorrelation chip response.

Similarly, the sine weighting function forces the QBL-MSKautocorrelation function to zero at times −T_(c)+ΔT_(c), ΔT_(c), and2T_(c)+ΔT_(c), so only the QBL-MSK terms at −T_(c)+ΔT_(c) andT_(c)+ΔT_(c) are considered for each sine-weighted QBL-MSKautocorrelation chip response. Using this information, the equations forthe serial I and Q signal may be rewritten as follows: $\begin{matrix}{{{{sx}\left( {nT}_{c} \right)} = {\sum\limits_{k = 0}^{N}\left\{ {{\left\lbrack {\sum\limits_{i = 0}^{{2M} - 1}{c_{i + {2{kM}}} \cdot \left\{ {{{g\left( {\Delta\quad T_{c}} \right)}{\delta\left( {n - \left\lbrack {i + {2{kM}}} \right\rbrack} \right)}} - {{g\left( {{{- 2}T_{c}} + {\Delta\quad T_{c}}} \right)}{\delta\left( {n + \quad 2 - \left\lbrack {i + {2{kM}}} \right\rbrack} \right)}} - {{g\left( {{2T_{c}} + {\Delta\quad T_{c}}} \right)}{\delta\left( {n - 2 - \left\lbrack {i + {2{kM}}} \right\rbrack} \right)}}} \right\}}} \right\rbrack \cdot {\cos\left( {\theta_{k} + \phi} \right)}} - {\left\lbrack \quad{\sum\limits_{i = 0}^{M - 1}{c_{i + {2{kM}}} \cdot \left\{ {{- {g\left( {{iT}_{c} + {\Delta\quad T_{c}}} \right)}}{\delta\left( {n - 1 - \left\lbrack {i + {2{kM}}} \right\rbrack} \right)}} \right\}}} \right\rbrack \cdot {\sin\left( {\theta_{k} + \phi} \right)}}} \right\}}}{and}} & \left( {{eqn}\quad 33} \right) \\{{{sy}\left( {nT}_{c} \right)} = {- {\sum\limits_{k = 0}^{N}\left\{ \left\lbrack {{\sum\limits_{i = 0}^{{2M} - 1}{c_{i + {2{kM}}} \cdot \left\{ {{{g\left( {\Delta\quad T_{c}} \right)}{\delta\left( {n - \left\lbrack {i + {2{kM}}} \right\rbrack} \right)}} - {{g\left( {{{- 2}T_{c}} + {\Delta\quad T_{c}}} \right)}{\delta\left( {n + 2 - \left( {n + 2 - \left\lbrack {i + {2{kM}}} \right\rbrack} \right) - {{g\left( {{2T_{c}} + {\Delta\quad T_{c}}} \right)}{\delta\left( {n - 2 - \left\lbrack {i + {2{kM}}} \right\rbrack} \right)}}} \right\}}}} \right\rbrack \cdot {\sin\left( {\theta_{k} + \phi} \right)}}} + {\left\lbrack {\sum\limits_{i = 0}^{M - 1}{c_{i + {2{kM}}} \cdot \left\{ {{{- {g\left( {{- T_{c}} + {\Delta\quad T_{c}}} \right)}}{\delta\left( {n + 1 - \left\lbrack {i + {2{kM}}} \right\rbrack} \right)}} + {{g\left( {T_{c} + {\Delta\quad T_{c}}} \right)}{\delta\left( {n - 1 - \left\lbrack {i + {2{kM}}} \right\rbrack} \right)}}} \right\}}} \right\rbrack \cdot {\cos\left( {\theta_{k} + \phi} \right)}}} \right) \right\}}}} & \left( {{eqn}\quad 34} \right)\end{matrix}$where δ(n) is the unit impulse function, which is equal to 1 for n equalto zero and equal to 0 for all other values of n. Despreading the serialI and Q signals and accumulating over a symbol, results in the followingequation for the despread I and Q symbol signals: $\begin{matrix}{{I\left( {kT}_{s} \right)} = {\sum\limits_{k = 0}^{N}\left\{ {{{\cos\left( {\theta_{k} + \phi} \right)}\left\lbrack {{2{M \cdot \alpha_{0}}} - {\sum\limits_{i = 2}^{{2M} - 3}{c_{i + {2{kM}}} \cdot \left\{ {{c_{i - 2 + {2{kM}}} \cdot \alpha_{- 2}} + {c_{i + 2 + {2{kM}}} \cdot \alpha_{2}}} \right\}}}} \right\rbrack} - \left\lbrack \quad{\sum\limits_{i = 0}^{1}{c_{i + {2{kM}}} \cdot \left\{ {{{c_{i - 2 + {2{kM}}} \cdot \alpha_{- 2}}{\cos\left( {\theta_{k - 1} + \phi} \right)}} + {{c_{{+ 2} + {2{kM}}} \cdot \alpha_{2}}{\cos\left( {\theta_{k} + \phi} \right)}}} \right\}}} \right\rbrack - \left\lbrack \quad{\sum\limits_{i = {{2M} - 2}}^{{2M} - 1}{c_{i + {2{kM}}} \cdot \left\{ {{{c_{i - 2 + {2{kM}}} \cdot \alpha_{- 2}}{\cos\left( {\theta_{k} + \phi} \right)}} + {{c_{i + 2 + {2{kM}}} \cdot \alpha_{2}}{\cos\left( {\theta_{k} + \phi} \right)}}} \right\}}} \right\rbrack - {{\sin\left( {\theta_{k} + \theta_{0}} \right)}\left\lbrack \quad{\sum\limits_{i = 1}^{{2M} - 2}{c_{i + {2{kM}}} \cdot \left\{ {{c_{i - 1 + {2{kM}}} \cdot \alpha_{- 1}} - {c_{i + 1 + {2{kM}}} \cdot \alpha_{1}}} \right\}}} \right\rbrack} + {c_{2{kM}} \cdot \left\lbrack {{{c_{{2{kM}} - 1} \cdot \alpha_{- 1}}{\cos\left( {\theta_{k - 1} + \phi} \right)}} - {{c_{{2{kM}} + 1} \cdot \alpha_{1}}{\cos\left( {\theta_{k + 1} + \phi} \right)}}} \right\rbrack}} \right\}}} & \left( {{eqn}\quad 35} \right) \\{{Q\left( {kT}_{s} \right)} = \quad{- {\sum\limits_{k = 0}^{N}{\left\{ {{{\sin\left( {\theta_{k} + \phi} \right)}\left\lbrack {{2{M \cdot \alpha_{0}}} - {\sum\limits_{i = 2}^{{2M} - 3}{c_{i + {2{kM}}} \cdot \left\{ {{c_{i + {2{kM}}} \cdot \alpha_{- 2}} + {c_{i + 2 + {2{kM}}} \cdot \alpha_{2}}} \right\}}}} \right\rbrack} - \left\lbrack \quad{\sum\limits_{i = 0}^{1}{c_{i + {2{kM}}} \cdot \left\{ {{{c_{i + {2{kM}}} \cdot \alpha_{- 2}}{\cos\left( {\theta_{k - 1} + \phi} \right)}} + {{c_{i + 2 + {2{kM}}} \cdot \alpha_{2}}{\cos\left( {\theta_{k} + \phi} \right)}}} \right\}}} \right\rbrack - \left\lbrack \quad{\sum\limits_{i = {{2M} - 2}}^{{2M} - 1}{c_{i + {2{kM}}} \cdot \left\{ {{{c_{i - 2 + {2{kM}}} \cdot \alpha_{- 2}}{\cos\left( {\theta_{k} + \phi} \right)}} + {{c_{i + 2 + {2{kM}}} \cdot \alpha_{2}}{\cos\left( {\theta_{k + 1} + \phi} \right)}}} \right\}}} \right\rbrack + {{\cos\left( {\theta_{k} + \theta_{0}} \right)}\left\lbrack \quad{\sum\limits_{i = 1}^{{2M} - 2}{c_{i + {2{kM}}} \cdot \left\{ {{c_{i - 1 + {2{kM}}} \cdot \alpha_{- 1}} - {c_{i + 1 + {2{kM}}} \cdot \alpha_{1}}} \right\}}} \right\rbrack} + {c_{2{kM}} \cdot \left\lbrack {{{c_{{2{kM}} - 1} \cdot \alpha_{- 1}}{\cos\left( {\theta_{k - 1} + \phi} \right)}} - {{c_{{2{kM}} + 1} \cdot \alpha_{1}}{\cos\left( {\theta_{k + 1} + \phi} \right)}}} \right\rbrack}} \right\}{where}}}}} & \left( {{eqn}\quad 36} \right) \\{\alpha_{n} = {{g\left( {{nT}_{c} + {\Delta\quad T_{c}}} \right)}.}} & \left( {{eqn}\quad 37} \right)\end{matrix}$

These equations show that the cross-correlation properties of thespreading sequence across the signal impact both the despread I and Qsymbol signals. As shown in these equations, the spreading code propertyfor 1 and 2 chip delay cross-correlation property for the 2M chipsimpact the despread I and Q signals. Detecting the first symbol anddropping the cross symbol spreading terms results in the followingequations for the first despread I and Q symbol signals: $\begin{matrix}{{{I(0)} = {{{\cos\left( {\theta_{0} + \phi} \right)}\left\lbrack {{2{M \cdot \alpha_{0}}} - {\left( {\alpha_{- 2} + \alpha_{2}} \right){\sum\limits_{i = 0}^{{2M} - 3}{c_{i} \cdot c_{i + 2}}}}} \right\rbrack} - {{\sin\left( {\theta_{0} + \phi} \right)}\left\lbrack {\left( {\alpha_{- 1} - \alpha_{1}} \right){\sum\limits_{i = 0}^{{2M} - 2}{c_{i} \cdot c_{i + 1}}}} \right\rbrack}}}{and}} & \left( {{eqn}\quad 38} \right) \\{{Q(0)} = {- {\left\{ {{{\sin\left( {\theta_{0} + \phi} \right)}\left\lbrack {{2{M \cdot \alpha_{0}}} - {\left( {\alpha_{- 2} + \alpha_{2}} \right){\sum\limits_{i = 0}^{{2M} - 3}{c_{i} \cdot c_{i + 2}}}}} \right\rbrack} + {{\cos\left( {\theta_{0} + \phi} \right)}\left\lbrack {\left( {\alpha_{- 1} - \alpha_{1}} \right){\sum\limits_{i = 0}^{{2M} - 2}{c_{i} \cdot c_{i + 1}}}} \right\rbrack}} \right\}.}}} & \left( {{eqn}\quad 39} \right)\end{matrix}$

These equations show that the spreading sequence properties and the chiptiming error, which impacts the α_(n) terms, affect the magnitude andphase of the despread I and Q symbol signals. The 2 chip delaycross-correlation for the spreading sequence reduces the magnitude ofthe desired term on both the I and Q signals. The 1 chip delaycross-correlation for the spreading sequence introduces a phase shiftsince it is orthogonal to the desired term on both the I and Q signals.From FIG. 9, the QBL-MSK autocorrelation value for the α⁻² and α₂ termsare less than or equal to 0.1, while the α⁻¹ and α₁ terms are as largeas 0.67. Since the α⁻¹ and α₁ terms are so much larger than the α⁻² andα₂ terms and they introduce the undesired phase shift, these equationsmay be simplified by dropping the α⁻² and α₂ terms.

Computer simulation results for 8 chips per symbol (M=4) verified thatthe α⁻² and α₂ terms may be dropped without significant degradation inperformance. Therefore, the phase correction process used by the presentinvention is based on only the α⁻¹ and α₁ terms. In another embodiment,however, this phase correction process may be easily modified toincorporate the α⁻² and α₂ terms.

Using only the α⁻¹ and α₁ terms (assuming α₀ is approximately 1) in thisexemplary embodiment reduces the despread first I and Q symbol signalsto the following: $\begin{matrix}{{{I(0)} = {{2{M \cdot {\cos\left( {\theta_{0} + \phi} \right)}}} - {{\sin\left( {\theta_{0} + \phi} \right)}\left\lbrack {\left( {\alpha_{- 1} - \alpha_{1}} \right){\sum\limits_{i = 0}^{{2M} - 2}{c_{i} \cdot c_{i + 1}}}} \right\rbrack}}}{and}} & \left( {{eqn}\quad 40} \right) \\{{Q(0)} = {- {\left\{ {{2{M \cdot {\sin\left( {\theta_{0} + \phi} \right)}}} + {{\cos\left( {\theta_{0} + \phi} \right)}\left\lbrack {\left( {\alpha_{- 1} - \alpha_{1}} \right){\sum\limits_{i = 0}^{{2M} - 2}{c_{i} \cdot c_{i + 1}}}} \right\rbrack}} \right\}.}}} & \left( {{eqn}\quad 41} \right)\end{matrix}$

Applying the first symbol I and Q equations to the despread I and Qsymbol signals results in the following equations for the despread I andQ symbol signals: $\begin{matrix}{\begin{matrix}{{I\left( {kT}_{s} \right)} = {{2{M \cdot {\cos\left( {\theta_{k} + \phi} \right)}}} - {\sin\left( {\theta_{k} + \phi} \right)}}} \\{\left\lbrack {\left( {\alpha_{- 1} - \alpha_{1}} \right){\sum\limits_{i = 0}^{{2M} - 2}{c_{i + {2{kM}}} \cdot c_{i + {2{kM}} + 1}}}} \right\rbrack} \\{= {{A(k)} \cdot {\cos\left( {\theta_{k} + \phi + {\gamma(k)}} \right)}}}\end{matrix}{and}} & \left( {{eqn}\quad 42} \right) \\{\begin{matrix}{{Q\left( {kT}_{s} \right)} = {- \left\{ {{2{M \cdot {\sin\left( {\theta_{k} + \phi} \right)}}} + {\cos\left( {\theta_{k} + \phi} \right)}} \right.}} \\\left. \left\lbrack {\left( {\alpha_{- 1} - \alpha_{1}} \right){\sum\limits_{i = 0}^{{2M} - 2}{c_{i + {2{kM}}} \cdot c_{i + {2{kM}} + 1}}}} \right\rbrack \right\} \\{{= {{- {A(k)}} \cdot {\sin\left( {\theta_{k} + \phi + {\gamma(k)}} \right)}}};}\end{matrix}{where}} & \left( {{eqn}\quad 43} \right) \\{{{A(k)} = \sqrt{{4M^{2}} + \left\lbrack {\left( {\alpha_{- 1} - \alpha_{1}} \right){\sum\limits_{i = 0}^{{2M} - 2}{c_{i + {2{kM}}} \cdot c_{i + {2{kM}} + 1}}}} \right\rbrack^{2}}}{and}} & \left( {{eqn}\quad 44} \right) \\{{\gamma(k)} = {{\tan^{- 1}\left\lbrack \frac{\left( {\alpha_{- 1} - \alpha_{1}} \right){\sum\limits_{i = 0}^{{2M} - 2}{c_{\quad{i + {2{kM}}}} \cdot c_{i + {2{kM}} + 1}}}}{2M} \right\rbrack}.}} & \left( {{eqn}\quad 45} \right)\end{matrix}$

The phase term γ(k) represents the phase shift produced by the chiptiming error and the spreading sequence property. Referring now to FIG.15, the despread I and Q symbol signals are sent to phase correctionmodule, generally designated as 171, to remove this phase error term andto recover the transmitted I and Q symbols.

As shown, the despread I and Q signals are first phase corrected usingthe spreading code property (SCP) and the chip timing error estimate forthe SYNC/serial probe function. For QPSK data modulation, the detected Iand Q symbols are obtained directly from the I and Q output of phasecorrection module 171. This assumes that coherent carrier phase trackingis performed on the signal to remove carrier frequency error and phaseerror. For DQPSK data modulation, differential detection is performed bydifferential detection module 182 to recover the I and Q symbols. DQPSKdemodulation does not require the carrier frequency and phase trackingneeded for QPSK.

Phase correction module 171 uses spreading code property (SCP) and chiptiming estimates to determine the proper phase correction term. Thespreading code property (SCP) is determined at spreading sequenceautocorrelation determination module 184 by generating a 1 chip delaycross-correlation property for the 2M chips used to spread the symbol.For symbol k, the spreading code property is the following:$\begin{matrix}{{{{SCP}(k)} = {\sum\limits_{i = {2{kM}}}^{{2M*{({k + 1})}} - 2}{c_{i} \cdot c_{i + 1}}}};} & \left( {{eqn}\quad 46} \right)\end{matrix}$where the chip values (c_(i)) equal −1 or +1 and the spreading is 2Mchips per symbol as shown in FIG. 10. For 8 chips per symbol, as anexample, M is equal to 4, which corresponds to 4 even and 4 odd chipsper symbol, resulting in the following spreading code property equation:$\begin{matrix}{{{SCP}(k)} = {\sum\limits_{i = {8*k}}^{{8*{({k + 1})}} - 2}{c_{i} \cdot {c_{i + 1}.}}}} & \left( {{eqn}\quad 47} \right)\end{matrix}$

The spreading code property {SCP(k)} determined at module 184 along withthe chip timing error information {X1, Y1, Y2, and Y3} from theSYNC/serial probe function of FIG. 13 are used to provide a phasecorrection term γ₁(k), which ideally equals γ(k). The SYNC/serial probefunction sets the chip timing error information across the message blockbetween the SYNC and serial probe or between two serial probes, whilethe spreading code property is calculated for each symbol at spreadingsequence module 184.

As an example, for 8 chips per symbol spreading, for a given symbol k,the value of SCP(k) takes on the value of −7, −5, −3, −1, 1, 3, 5, or 7.Using the spreading code property value for each symbol along with thechip timing estimation {X1, Y1, Y2, and Y3}, the proper phase correctionfor the symbol is selected based on a look up table, such as TABLE 1,designated as correction table 186 in FIG. 15. The table phasecorrection output, γ₁(k), is an estimate of the actual phase error γ(k).

The phase corrected I and Q symbol signals {I_(c)(k) and Q_(c)(k)} aregiven by the following equations: $\begin{matrix}{\begin{matrix}{{I_{c}\left( {kT}_{s} \right)} = {{A(k)} \cdot \left\lbrack {{{\cos\left( {\theta_{k} + \phi} \right)} \cdot {\cos\left( {\gamma_{1}(k)} \right)}} + \sin} \right.}} \\\left. {\left( {\theta_{k} + \phi + {\gamma(k)}} \right) \cdot {\sin\left( {\gamma_{1}(k)} \right)}} \right\rbrack \\{= {{A(k)} \cdot {\cos\left( {\theta_{k} + \phi + {\gamma(k)} - {\gamma_{1}(k)}} \right)}}}\end{matrix}{and}} & \left( {{eqn}\quad 48} \right) \\\begin{matrix}{{Q_{c}\left( {kT}_{s} \right)} = {{A(k)} \cdot \left\lbrack {{{\sin\left( {\theta_{k} + \phi} \right)} \cdot {\cos\left( {\gamma_{1}(k)} \right)}} - \cos} \right.}} \\\left. {\left( {\theta_{k} + \phi + {\gamma(k)}} \right) \cdot {\sin\left( {\gamma_{1}(k)} \right)}} \right\rbrack \\{= {{A(k)} \cdot {{\sin\left( {\theta_{k} + \phi + {\gamma(k)} - {\gamma_{1}(k)}} \right)}.}}}\end{matrix} & \left( {{eqn}\quad 49} \right)\end{matrix}$

As these equations show, if γ₁(k) equals γ(k), the phase error term goesto zero. Since phase correction table 186 has finite values, there is asmall phase error term as shown in the improved BER performance curve ofFIG. 4. To further simplify the phase correction process, the simplifiedcosine and sine tables, shown in TABLES 2 and 3, respectively, may beused in the phase correction process performed by phase correctionmodule 171.

Implementation of the phase correction for each symbol is performed byphase correction module 171 using phase rotators, as shown in FIG. 15.In another embodiment, such as a rake receiver, phase correctionoperation may be performed for each rake tap. The phase correctionparameters {X1, Y1, Y2, and Y3} for each independent rake tap along withthe spreading code property for each symbol may be used to select theproper phase correction for each symbol on each rake tap in thedemodulator.

Returning to FIG. 15, the despread I and Q signals, I(k) and Q(k),respectively, enter phase correction module 171 and are multiplied byphase correction signal cos [γ₁(k)] at mixers 170 and 180 and by phasecorrection signal sin [γ₁(k)] at mixers 174 and 176. The resultingsignals from mixers 170 and 174 are then combined by summer 172 and theresulting signals from mixers 176 and 180 are combined by summer 178.

After phase correction, the I and Q data symbols are determined. ForQPSK data modulation, the detected I and Q symbols are obtained directlyfrom the I and Q outputs of phase correction module 171. This assumesthat coherent carrier phase tracking is performed on the signal toremove carrier frequency error and phase error (φ given in equations 48and 49). The corrected I and Q symbol signals {I_(c)(k) and Q_(c)(k)}are each independently compared against zero to determine if a +1 (logic0) or −1 (logic 1) was received for that corresponding symbol. For DQPSKdemodulation, the corrected I and Q symbol signals {I_(c)(k) andQ_(c)(k)} are processed by DQPSK differential detector 182 to determinethe detected I and Q symbol signals {I_(d)(k) and Q_(d)(k)}. The I and Qdetected symbol signals output from the differential detector are eachindependently compared against zero to determine if a +1 (logic 0) or −1(logic 1) was received for that corresponding symbol.

In summary, an aspect of the present invention reduces the BERperformance degradation associated with QPSK or DQPSK data modulation onserial direct sequence spread waveforms, such as QBL-MSK, by providing aphase correction term based on the spreading sequence property and anestimate of the chip timing error. The phase correction term may also beused to enhance QPSK or DQPSK data detection for receivers operating ata sampling rate equal to the chip rate or for receivers operating atsampling rates greater than twice the chip rate. Operation at differentsampling rates simply requires an appropriate change in the phasecorrection table.

The phase correction process described herein for QPSK/DQPSK may beexpanded to include higher orders of phase modulation, such as 8-PSK andDifferential 8-PSK. Also, the phase correction technique may be used toreduce the BER performance degradation associated with using π/4-QPSK ordifferential π/4-QPSK data modulation on a serial direct sequence spreadwaveform, such as QBL-MSK.

In addition to enabling changes to the data modulation type, the phasecorrection process may be used by applying serial formatting to otherquadrature spreading modulation waveforms, such as Offset QuadraturePhase Shift Keying (OQPSK), Minimum Shift Keying (MSK), Gaussian MSK,Tamed Frequency Modulation (TFM), Intersymbol Jitter Free OffsetQuadrature Phase Shift Keying (IJF-OQPSK), Raised Cosine Filtered OffsetQuadrature Phase Shift Keying (RC-OQPSK), and bandwidth efficientContinuous Phase Modulation (CPM) schemes.

For other similar and non-similar disclosures, please refer to thefollowing five applications filed on the same day as this application.These five applications are TBD (and, respectively, correspond to thefollowing five provisional applications 60/703,180; 60/703,179;60/703,373; 60/703,320 and 60/703,095). These applications are allincorporated herein by reference in their entireties.

Although illustrated and described herein with reference to certainspecific embodiments, the present invention is nevertheless not intendedto be limited to the details shown. Rather, various modifications may bemade in the details within the scope and range of equivalents of theclaims and without departing from the spirit of the invention. TABLE 1Correction Phase (degrees) for Different Spreading Code PropertiesCorrection Phase (degrees) for the Y1 = X2 Y2 = X4 Y3 = X6 Different1*Tc Delay Summation Values ΔTc X1 OR X3 OR X5 OR X7 7 5 3 1 −1 −3 −5 −7−0.5000 0 1 1 0 −5 −3 −2 0 0 2 3 5 −0.4375 0 1 1 0 −5 −3 −2 0 0 2 3 5−0.3750 0 1 0 0 −15 −10 −5 −2 2 5 10 15 −0.3125 0 1 0 0 −15 −10 −5 −2 25 10 15 −0.2500 0 1 0 0 −15 −10 −5 −2 2 5 10 15 −0.1875 0 0 0 1 15 10 52 −2 −5 −10 −15 −0.1250 0 0 0 1 15 10 5 2 −2 −5 −10 −15 −0.0625 0 0 0 05 3 2 0 0 −2 −3 −5 0.0000 0 0 0 0 5 3 2 0 0 −2 −3 −5 0.0625 1 0 0 0 −5−3 −2 0 0 2 3 5 0.1250 1 0 0 1 −15 −10 −5 −2 2 5 10 15 0.1875 1 0 0 1−15 −10 −5 −2 2 5 10 15 0.2500 1 1 0 0 15 10 5 2 −2 −5 −10 −15 0.3125 11 0 0 15 10 5 2 −2 −5 −10 −15 0.3750 1 1 0 0 15 10 5 2 −2 −5 −10 −150.4375 1 1 1 0 5 3 2 0 0 −2 −3 −5 0.5000 1 1 1 0 5 3 2 0 0 −2 −3 −5

TABLE 2 Correction Phase (Simplified Cosine Terms) for DifferentSpreading Code Properties Simplified Cosine Phase Correction Term forthe Chip Timing Y1 = X2 Y2 = X4 Y3 = X6 Different Spreading CodeProperties ΔTc X1 OR X3 OR X5 OR X7 7 5 3 1 −1 −3 −5 −7 −0.5000 0 1 1 01 1 1 1 1 1 1 1 −0.4375 0 1 1 0 1 1 1 1 1 1 1 1 −0.3750 0 1 0 0 0.968750.984375 1 1 1 1 0.984375 0.96875 −0.3125 0 1 0 0 0.96875 0.984375 1 1 11 0.984375 0.96875 −0.2500 0 1 0 0 0.96875 0.984375 1 1 1 1 0.9843750.96875 −0.1875 0 0 0 1 0.96875 0.984375 1 1 1 1 0.984375 0.96875−0.1250 0 0 0 1 0.96875 0.984375 1 1 1 1 0.984375 0.96875 −0.0625 0 0 00 1 1 1 1 1 1 1 1 0.0000 0 0 0 0 1 1 1 1 1 1 1 1 0.0625 1 0 0 0 1 1 1 11 1 1 1 0.1250 1 0 0 1 0.96875 0.984375 1 1 1 1 0.984375 0.96875 0.18751 0 0 1 0.96875 0.984375 1 1 1 1 0.984375 0.96875 0.2500 1 1 0 0 0.968750.984375 1 1 1 1 0.984375 0.96875 0.3125 1 1 0 0 0.96875 0.984375 1 1 11 0.984375 0.96875 0.3750 1 1 0 0 0.96875 0.984375 1 1 1 1 0.9843750.96875 0.4375 1 1 1 0 1 1 1 1 1 1 1 1 0.5000 1 1 1 0 1 1 1 1 1 1 1 1

TABLE 3 Correction Phase (Simplified Sine Terms) for Different SpreadingCode Properties Chip Simplified Sine Phase Correction Term for theTiming Y2 = X4 Y3 = X6 Different Spreading Code Properties ΔTc X1 Y1 =X2 OR X3 OR X5 OR X7 7 5 3 1 −1 −3 −5 −7 −0.5000 0 1 1 0 −0.09375−0.0625 −0.03125 0 0 0.03125 0.0625 0.09375 −0.4375 0 1 1 0 −0.09375−0.0625 −0.03125 0 0 0.03125 0.0625 0.09375 −0.3750 0 1 0 0 −0.25−0.1875 −0.09375 0.03125 0.03125 0.09375 0.1875 0.25 −0.3125 0 1 0 0−0.25 −0.1875 −0.09375 −0.03125 0.03125 0.09375 0.1875 0.25 −0.2500 0 10 0 −0.25 −0.1875 −0.09375 −0.03125 0.03125 0.09375 0.1875 0.25 −0.18750 0 0 1 0.25 0.1875 0.09375 0.03125 −0.03125 −0.09375 −0.1875 −0.25−0.1250 0 0 0 1 0.25 0.1875 0.09375 0.03125 −0.03125 −0.09375 −0.1875−0.25 −0.0625 0 0 0 0 0.09375 0.0625 0.03125 0 0 −0.03125 −0.0625−0.09375 0.0000 0 0 0 0 0.09375 0.0625 0.03125 0 0 −0.03125 −0.0625−0.09375 0.0625 1 0 0 0 −0.09375 −0.0625 −0.03125 0 0 0.03125 0.06250.09375 0.1250 1 0 0 1 −0.25 −0.1875 −0.09375 −0.03125 0.03125 0.093750.1875 0.25 0.1875 1 0 0 1 −0.25 −0.1875 −0.09375 −0.03125 0.031250.09375 0.1875 0.25 0.2500 1 1 0 0 0.25 0.1875 0.09375 0.03125 −0.03125−0.09375 −0.1875 −0.25 0.3125 1 1 0 0 0.25 0.1875 0.09375 0.03125−0.03125 −0.09375 −0.1875 −0.25 0.3750 1 1 0 0 0.25 0.1875 0.093750.03125 −0.03125 −0.09375 −0.1875 −0.25 0.4375 1 1 1 0 0.09375 0.06250.03125 0 0 −0.03125 −0.0625 −0.09375 0.5000 1 1 1 0 0.09375 0.06250.03125 0 0 −0.03125 −0.0625 −0.09375

1. In a receiver, a method of correcting phase error of a phase shiftkeyed (PSK) signal, comprising the steps of: (a) receiving a signalmodulated by a spreading sequence; (b) despreading the received signalusing a receiver spreading sequence similar to the spreading sequence ofstep (a); (c) calculating a crosscorrelation profile between thereceiver spreading sequence and the received signal; (d) calculating anautocorrelation profile of the receiver spreading sequence to determinea spreading code property (SCP); (e) estimating a timing error inalignment between the autocorrelation and the crosscorrelation profiles;and (f) correcting a phase error of the signal despread in step (c), byusing the SCP and the estimated timing error.
 2. The method of claim 1,wherein the received signal includes pulses at a chip rate, and step (a)includes: demodulating the received signal with a carrier signal to forma baseband signal, sampling the baseband signal at a rate greater thanthe chip rate, and step (b) includes: despreading the baseband signal ata rate that is the same as the chip rate.
 3. The method of claim 2,wherein demodulating includes forming inphase (I) and quadrature (Q)baseband signals, and despreading includes despreading the I and Qbaseband signals using only one receiver spreading sequence.
 4. Themethod of claim 1, wherein the received signal includes pulses at a chiprate, and between step (a) and step (b) the following steps areperformed: phase rotating the received signal to form seriallydemodulated I and Q baseband signals, each sampled at a rate greaterthan the chip rate, reducing the sampled I and Q baseband signals by atleast a factor of ½ to form decimated I and Q baseband signals, eachsampled at the chip rate, and despreading the decimated I and Q basebandsignals using the receiver spreading sequence at the chip rate.
 5. Themethod of claim 4, wherein despreading the decimated I and Q basebandsignals is performed using a single receiver spreading sequence.
 6. Themethod of claim 1, wherein step (a) includes demodulating the receivedsignal to form I and Q baseband signals, and step (c) includesseparately crosscorrelating the I and Q baseband signals with a sequenceof chips of the receiver spreading sequence to form an I correlatedsignal and a Q correlated signal.
 7. The method of claim 6 wherein the Iand Q correlated signals are summed to form the crosscorrelationprofile.
 8. The method of claim 7 wherein prior to summing, the I and Qcorrelated signals are individually squared.
 9. The method of claim 1wherein step (d) includes time shifting the receiver spreading sequenceagainst the same receiver spreading sequence by a maximum time of twochip periods of the receiver spreading sequence.
 10. The method of claim9 wherein the time shifting is a maximum time of one chip period. 11.The method of claim 1 wherein the received signal includes data symbols,each symbol including an integer number of chips, and step (d) includesdetermining the SCP for at least one symbol.
 12. The method of claim 11wherein for 8 chips per symbol, the SCP for a data symbol takes onvalues of −7, −5, −3, −1, 1, 3, 5 or
 7. 13. The method of claim 1wherein step (e) includes the steps of: locating a peak value of thecrosscorrelation profile as COR (nTc), where Tc is a chip period and nis a sample number; determining a value of a sample of thecrosscorrelation profile after the peak value, as COR ([n+1]Tc) and avalue of another sample of the crosscorrelation profile before the peakvalue, as COR ([n−1]Tc); and using the values of COR (nTc), COR([n−1]Tc) and COR ([n+1]Tc) to estimate the timing error.
 14. The methodof claim 1 wherein an estimated timing error, estimated in step (e), andthe SCP, determined in step (d), are used to select a phase error storedin a look-up-table (LUT), and step (f) uses the selected phase error tocorrect the phase error of the signal despread in step (c).
 15. Themethod of claim 1 wherein step (f) includes using values of degrees, orvalues of sine/cosine terms, stored in a LUT to correct the phase errorof the signal despread in step (c).
 16. The method of claim 1 whereinstep (b) includes despreading the received signal into a despread I andQ baseband signals, and step (f) includes correcting the phase error ofthe despread I and Q baseband signals using values of sine and cosineterms stored in a LUT to form phase corrected I and Q symbols forquadrature PSK (QPSK) detection.
 17. The method of claim 1 wherein thereceived signal includes one of QPSK, differential QPSK, QBL-MSK, 8-PSK,differential 8-PSK, π/4-QPSK, differential π/4-QPSK, BPSK, ordifferential BPSK.
 18. In a receiver, a method of serially demodulatinga phase shift keyed (PSK) signal, comprising the steps of: (a) receivinga PSK signal modulated by a spreading sequence at a chip rate; (b)dividing the PSK signal into an inphase (I) signal and a quadrature (Q)signal at a sampling rate greater than the chip rate; (c) rotatingphases of the I signal and the Q signal at the sampling rate of step (b)to obtain serially demodulated I and Q signals; (d) determining chipsynchronization time for the serially demodulated I and Q signals; (e)decimating the serially demodulated I and Q signals, based on thedetermined chip synchronization time, so that the serially demodulated Iand Q signals are sampled at the chip rate; and (f) despreading thedecimated I and Q signals by mixing the decimated I and Q signals with asingle spreading sequence.
 19. The method of claim 18 wherein the PSKsignal includes one of QPSK, differential QPSK, 8-PSK, differential8-PSK, π/4-QPSK, differential π/4-QPSK, BPSK, or differential BPSK. 20.A receiver comprising a despreading module for despreading a basebandsignal, using a spreading sequence generated by a code generator, acrosscorrelation module for calculating a crosscorrelation profilebetween the baseband signal and the spreading sequence, anautocorrelation module for calculating an autocorrelation profile of thespreading sequence to determine a SCP value of the spreading sequence,an error timing estimating module, coupled to the crosscorrelation andautocorrelation modules, for estimating an alignment error between theautocorrelation profile and the crosscorrelation profile, and a phasecorrection module, coupled to the error timing estimating module and thedespreading module, for correcting a phase error in the despreadbaseband signal.
 21. The receiver of claim 20 wherein the phasecorrection module is configured to extract phase error correction valuesfrom a LUT, the LUT including the phase error correction values based onSCP values and alignment errors between the autocorrelation andcrosscorrelation profiles.
 22. The receiver of claim 20 including ademodulator for mixing a carrier signal with a received signal,including a chipping rate of pulses, to form a demodulated signal, ananalog-to-digital converter (ADC) configured to sample the demodulatedsignal, at a sampling rate greater than the chipping rate, to form asampled signal, a phase rotator for phase rotating the sampled signal toform a serially demodulated signal at the same sampling rate, and adecimator for reducing the sampling rate of the serially demodulatedsignal to form the baseband signal.
 23. The receiver of claim 22 whereinthe baseband signal includes a baseband I signal and a baseband Qsignal, and the same spreading sequence is used to despread the basebandI and Q signals.
 24. The receiver of claim 20 wherein the phasecorrection module includes multipliers for multiplying the despreadbaseband signal with sine and cosine values extracted from a LUT. 25.The receiver of claim 20 wherein the baseband signal is one of QPSK,differential QPSK, QBL-MSK, 8-PSK, differential 8-PSK, π4-QPSK, ordifferential π/4-QPSK.